Electronic inhomogeneity and phase fluctuation in one-unit-cell FeSe films

One-unit-cell FeSe films on SrTiO3 substrates are of great interest owing to significantly enlarged pairing gaps characterized by two coherence peaks at ±10 meV and ±20 meV. In-situ transport measurement is desired to reveal novel properties. Here, we performed in-situ microscale electrical transport and combined scanning tunneling microscopy measurements on continuous one-unit-cell FeSe films with twin boundaries. We observed two spatially coexisting superconducting phases in domains and on boundaries, characterized by distinct superconducting gaps (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta }_{1}$$\end{document}Δ1~15 meV vs. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta }_{2}$$\end{document}Δ2~10 meV) and pairing temperatures (Tp1~52.0 K vs. Tp2~37.3 K), and correspondingly two-step nonlinear \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V \sim {I}^{\alpha }$$\end{document}V~Iα behavior but a concurrent Berezinskii–Kosterlitz–Thouless (BKT)-like transition occurring at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${T}_{{{{{{\rm{BKT}}}}}}}$$\end{document}TBKT~28.7 K. Moreover, the onset transition temperature \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${T}_{{{{{{\rm{c}}}}}}}^{{{{{{\rm{onset}}}}}}}$$\end{document}Tconset~54 K and zero-resistivity temperature \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${T}_{{{{{{\rm{c}}}}}}}^{{{{{{\rm{zero}}}}}}}$$\end{document}Tczero~31 K are consistent with Tp1 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${T}_{{{{{{\rm{BKT}}}}}}}$$\end{document}TBKT, respectively. Our results indicate the broadened superconducting transition in FeSe/SrTiO3 is related to intrinsic electronic inhomogeneity due to distinct two-gap features and phase fluctuations of two-dimensional superconductivity.

The 1 UC FeSe films on SrTiO3(001) consist of two types of domain boundaries, i.e. line defects under low Se flux with strong interface coupling and apparent bright twin boundaries under high Se flux with weakened interface coupling.As shown in Fig. S1a, under strong interface coupling limit, the domains in 1 UC FeSe film are separated by unidirectional line defects of Fe vacancies, wherein the outer gap reaches at 20 meV in maximum.Around line defects, the superconductivity gets suppressed 3 .The gap magnitude also decreases with reduced domain size.Thus, 1 UC FeSe films with line defects boundaries show a nearly Gaussian-distributed spatial gap distribution 2 , regardless of the value of gap magnitude, as shown in Fig. S1b.The different statistical results in locations H and M demonstrate the inhomogeneity in millimeter-scale.Whereas, under weakened interface coupling, the domains in 1 UC FeSe film are separated by bright twin boundaries, which are also FeSe films with compressed lattice, as shown in Fig. S1c.Without the dense line defects, 1 UC FeSe films with twin boundaries exhibit two typical superconducting gaps, namely ~15 meV in the domain and ~10 meV on twin boundaries.The representative gap distribution, as shown in Fig. S1d, is extracted from the sample in this study, which is also consistent with a previous study 4 .

Table S1 | Dynes-fitting parameters [Δ(T) and Γ(T)
] for fitting the spectra in Fig. S3b Table S2 | Dynes-fitting parameters [Δ(T) and Γ(T)] for fitting the spectra in Fig. S3f The BCS fitting of dI/dV spectra was conducted using Dynes function 5 .Each spectrum is first normalized by dividing a polynomial background fit and then fitted using Dynes function.Figure S3a,b represent the raw dI/dV spectra in domain and the fitting results, respectively.Besides, the ZBC shows a linear temperature dependence, as shown in Fig. S3c, giving a Tp ~ 51 K when ZBC=1, which is consistent with the gap closing temperature.Figure S3d shows another dataset of the original dI/dV spectra, demonstrating the repeatability and reliability of the results.Figure S3e,f represent the raw dI/dV spectra on twin boundaries and the fitting results, respectively.The spectral broadening Γ is a parameter in the Dynes fitting, which is related with the quasiparticle lifetime.Tables S1 and S2 show Γ used for fitting the spectra in Figs.S3b and S3f at different temperatures, respectively.
Figure S4 indicates that the Nb-doped SrTiO3 substrate has no influence on the measurements of superconducting transition in 1 UC FeSe films at low temperature.Au electrodes were deposited on the SrTiO3 substrate before conducting the measurements, because the electrical connection between the micro-four-point probes and the substrate can hardly be reached by direct contact.Due to the spread of Au atoms while passing through the mask, the actual measured distance is much shorter than 5 μm.

Table S3 | Comparison of representative Tc measurements on FeSe/SrTiO3(001) across different techniques
There are a lot of ex-situ and in-situ measurements on 1 UC FeSe/SrTiO3 in recent years, however, the consensus on its Tc has not been reached for the time being.Table S3 presents discrepancies on Tc even with the same measurement technique, which is probably due to different sample quality, such as preparation conditions, capping layers and types of domain boundaries.Reference 8 shows that different annealing conditions give different superconducting gaps, and larger gaps usually have higher closing temperatures.This feature of 1 UC FeSe demonstrates the importance of combining STM/STS and in-situ microscale transport measurements, enabling to know the sample status down to atomic scale.Overall, previous studies suggest the most common results that the gap closing temperature is ~65 K,  c zero ranges from 20 K to 29 K and  c onset ranges from 40 K to 53 K. Compared with the gap closing temperature ~ 52 K in this study, 65 K is likely obtained on FeSe films with strong interface coupling, featured by line defects domain boundaries and larger superconducting gaps.Besides,  c zero in this study is higher than 30 K, demonstrating the good sample quality and improved homogeneity under micro-scale measurements.Our result indicates that  c onset is consistent with the pairing temperature.Despite the different definition of  c onset , the relatively low  c onset in previous studies may be caused by the influence of capping layers or inhomogeneity 19,20 .
Figure S5 shows a blue-shifted kink of valence band on twin boundaries, compared with FeSe films within the domain.This system allows MBE growth, STM characterization, electrode deposition and micro-four-point probes (M4PP) electrical transport measurement to be performed under the same ultra-high vacuum.Our experiments were conducted in this system.Figures S7a,b show the SEM images of the M4PP and Au electrodes, respectively.Each M4PP chip consists of six probes, where four probes are used for transport measurement and two probes are for backup.The width of each probe is 5 μm.The distance between adjacent probes is also 5 μm.The electrodes match well with the M4PP. Figure S7c shows the electrical circuit for transport measurement.Four probes are electrically connected to a Keithley 6221 DC Sourcemeter and a Keithley 2182A Nanovoltmeter, respectively.Based on the DC current-reversal technique, a built-in Pulse Delta measurement mode of the nanovoltmeter is used to cancel the effects of thermoelectric potentials, which are generated by thermal differences between the junctions of probes and the sample.Specifically, the 2182A Nanovoltmeter performs the first voltage measurement ( 1 ) while sourcing a pulsed DC current (I), and performs the second voltage measurement ( 2 ) while sourcing a reversed current (-I).Then the final voltage is calculated as ( 1 −  2 )/2.Moreover, the pulsed current could avoid heating effects during measurements.Figure S7d shows the optical image of the measurement process.Monitored by the optical microscope, we can locate the measurement area at the micro scale.Note that transport measurements in this paper were conducted directly on the sample surface, as shown in Fig. 2, even though electrodes could facilitate keeping good contacts while varying temperature.This is because electrodes suppress the superconductivity of 1 UC FeSe films.

Fig. S1 |
Fig. S1 | The STM morphology and statistics on gap magnitude for 1 UC FeSe film with a-b (extracted form literatures 1,2), line defects and c-d, bright twin boundaries.

Fig. S3 |
Fig. S3 | Fitting results of dI/dV spectra.a, The original dI/dV spectra taken in domain at different temperatures.The triangles mark the coherence peak.Above 32 K, no obvious kink can be observed.b, Normalized spectra (open symbols) and BCS fittings (solid curves) at each temperature.c, The temperature dependence of the zero bias conductance (ZBC) extracted from the dI/dV spectra in b.The error bars are from the s.d. of the fittings.d, another dataset of original dI/dV spectra taken in domain.e, The original dI/dV spectra taken on twin boundaries.f, Normalized spectra (open symbols) and BCS fittings (solid curves) at each temperature.

Fig. S5 |
Fig. S5 | Comparison of large-energy-scale dI/dV spectra (VS = 0.4 V, It = 100 pA) of FeSe films within the domain and on twin boundaries.

Fig. S7 |
Fig. S7 | Illustration of in-situ micron-scale electrical transport measurements.a, Scanning electron microscopy (SEM) image of the M4PP.b, SEM image of Au electrodes.c, Electrical circuit for transport measurement.d, Optical image of the measurement process.